Introduction:
(Note: If you know how DSL works, you can jump to the next section!)
Most of the internet users nowadays are using DSL connections. DSL stands for Digital Subscriber Line which provides internet over telephone lines. DSL uses ADSL Routers or ADSL Modems. Here is a layman diagram of how DSL works:

Whenever a user turns on their DSL modem, they are connected to the DSLAM which is usually placed inside ISP Exchange. Each DSLAM has the capacity to connect with thousands of DSL users. In above image, it looks like a small box but actually it is much bigger:

DSLAM is responsible for checking the condition of telephone line and assures that a stable connection can be maintained. It also holds some properties for each telephone line. The Download and Upload Rate you see in your modem status page are also set by DSLAM. Once the DSLAM connection is established, the DSL light on some modems is turned on.

Now the modem sends Internet Access request to the BRAS server. This request contains the DSL username and password which is saved in the DSL modem settings. The login is usually set by the lineman when they install a new DSL connection. The BRAS server is directly connected with the central RADIUS server which contains login information of all DSL users. The RADIUS server also contains a list of IP Addresses which are not used by others. If the login sent by modem is valid, RADIUS server responds with one IP Address from the IP Address list. Once the modem receives the IP Address, an internet connection is established and the internet light on modem is turned on:

That was some lengthy introduction about DSL and its working for non-technical people!